If you want the angle to be something different from 90º or 45º and you need the exact length of the exterior to be something specific and you don't want to be changing the transformation orientation then I would install the Tiny CAD addon. It lets you create a vertex where 2 edges intersect.
With that, you can select the face you want to extrude and duplicate it first, then rotate it using one of the outside vertices as the pivot and then extrude it along it normal. This gives you complete control on the length of the wall.
This will leave you with 2 wall sections that are intersecting. You can now select one of the pairs of edges that are intersecting at the top and bottom and use Tiny CAD to place a vertex where they do. Then merge the ends of those edges into the newly created vertex. Repeat this for the bottom and/or any other edge loops the wall has.
This leaves you with the unchanged thickness and the controlled length of extruded segment. But it also creates some interior faces and overlapping vertices so when you are done, select and delete the interior faces, merge all vertices by distance and recalculate the normals.
On another note, if you don't care about precision that much and only need it to 'look' right you can use the Shear tool in the tools bar to rotate the edgeloop in the middle until it looks right